Messier Marathon
Nov 13, 2014
Messier Marathon
• Assignment 15 complete (10% penalty/day if you're late)
• Second mid-term• Wednesday April 23rd• Covers chapters 5, 10 and 11• Revise!• NOTE: today I will mainly go through math - but
most of the points on the exam come from the multiple choice sections - re-read these Chapters!!!
• extra office hours 2pm - 4pm tomorrow (Tuesday)
• Lab as usual this week• Honours section meet after this lecture
Admin:
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Review: powers of 10
• 101=10• 102=1010=100• 103=101010=1000• 104=10101010=10000
powers of 10
• 101=10• 100=10/10=1• 10-1=10/10/10=0.1• 10-2=10/10/10/10=0.01
An example: powers of 10
• To multiply, add the exponents• 103104=107
• To divide, subtract the exponents• 103 / 104=10-1
• To raise to a power, multiply exponents• (103)4 = 1012
• sqrt(x) = x1/2
Scientific notation
• 3000=31000=3103
• 0.0002 = 20.0001=210-4
• 210-4 3103
= 2 3 10-4 103 = 6 10-1
• (3 108)2
= 9 1016
Finding a ratio(See Appendix C.5)
• What if you want to compare two quantities?
• e.g. The average density of Earth is 5.52 g/cm3, that of Jupiter is 1.33 g/cm3. How much more dense is Earth than Jupiter?
• 5.52/1.33=4.15 times as dense.
Finding a ratio
• What if the two quantities involve an equation?
• e.g. the mass-energy of a 1kg mass m1, is 91016 Joules. What is the mass-energy of a 3kg mass?
1
3
1
2
21
22
1
2
m
m
m
m
E
E
cm
cm
E
E
does it make sense?
425.0
1
1
11
1
4
4
2
22
2
1
1
2
2
2
12
1222
1
22
21
22
1
2
d
d
b
b
d
dd
dd
d
dL
dL
b
b
d
d
d
d
• Earth is about 150 million kilometers from the Sun, and the apparent brightness of the Sun in our sky is about 1300 watts/m2 . Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at 1/2 the distance?
24 d
Lb
does it make sense???
d1=1d2=0.5
What if it were located 7 times the distance?
often don't need to memorize equations!!!
Ch. 5 Summary of Mathematics I f = c
= wavelength, f = frequencyc = 3.00 108 m/s = speed of light
E = h f = photon energyh = 6.626 10−34 joule s
Given any one of E, f, or you should be able to calculate the others
example: what is the energy of a photon with a wavelength of 300nm ?
E=h c/(1eV=1.610-19J)
Properties of Thermal Radiation1. Hotter objects emit more light at all frequencies per
unit area.
2. Hotter objects emit photons with a higher average energy (shorter wavelength).
Ch.5 Summary of Mathematics II1. Hotter objects emit more light at all frequencies per
unit area.
2. Hotter objects emit photons with a higher average energy.
)Kelvinwatt/(m107.5
area power/unit emitted428
4
T
nm)Kelvin(
000,900,2max T
Given the temperature of an object, you should be able to calculate the emitted power/unit area and the peak wavelength (see "cosmic calculations 5.1"). Given the peak wavelength, you should be able to calculate the temperature. E.g. Sun~6000K
Ch. 5 Summary of Mathematics III
• Doppler shift
rest
restshift
c
v
Given the wavelength of spectral lines, you should be able to tell if an object is moving away or towards you, and at what speed (see "cosmic calculations 5.2").
• In hydrogen, the transition from level 1 to level 2 has a rest wavelength of 121.6 nm. Suppose you see this line at a wavelength of 120.5nm in Star A and at 121.3nm in Star B.
• Calculate speed of Star A. • 2710 km/s
• Is it moving toward or away from us• toward us
• Calculate speed of star B• 740 km/s
• toward us
Math question
Features of a Spectrum
• By carefully studying the features in a spectrum, we can learn a great deal about the object that created it.
What is this object?
Reflected Sunlight: Continuous spectrum of visible light is like the Sun’s except that some of the blue light has been absorbed—object must look red
What is this object?
Thermal Radiation: Infrared spectrum peaks at a wavelength corresponding to a temperature of 225 K
What is this object?
Carbon Dioxide: Absorption lines are the fingerprint of CO2 in the atmosphere
What is this object?
Ultraviolet Emission Lines: Indicate a hot upper atmosphere
What is this object?
Mars!
The relationship between apparent brightness and luminosity depends on distance:
Luminosity Brightness = 4π (distance)2
We can determine a star’s luminosity if we can measure its distance and apparent brightness:
Luminosity = 4π (distance)2 (Brightness)
Ch. 11 Summary of Mathematics I
Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright.B. It would be only 1/6 as bright.C. It would be only 1/9 as bright.D. It would be three times as bright.
Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright.B. It would be only 1/6 as bright.C. It would be only 1/9 as bright.D. It would be three times as bright.
Math Question
The sun's measured apparent brightness is 1.36103 W/m2 at Earth's distance from the sun (1 AU = 1.51011m). What is the Sun's Luminosity?
24 d
Lb
Math Question
The sun's measured apparent brightness is 1.36103 W/m2 at Earth's distance from the sun (1 AU = 1.51011m). What is the Sun's Luminosity?
24 d
Lb
= 3.81026 W
Parallax and Distance
p = parallax angle
d (in parsecs) = 1
p (in arcseconds)
d (in light-years) = 3.26 1
p (in arcseconds)
(by definition)
Ch. 11 Summary of Mathematics II
Parallax and Distance
What's the distance of a star with a parallax angle of 1 arcsecond?
d= 1parsec =3.26 light years
What's the distance of a star with a parallax angle of 2 arcseconds?
d= 0.5parsecs =1.63 light years
NOTE: bigger angle means star is closer
Alpha Centauri: parallax angle 0.7420.
Ch. 11 Summary of Mathematics II
Sirius A has a luminosity of 26LSun and a surface temperature of about 9400K. What is its radius?
LSun=3.81026W
Ch. 11 Summary of Mathematics II
9
157
27
48
26
4
42
1030.1
108.7102.7
109.9
9400107.514.34
108.326
4
4
r
r
T
Lr
TrL
The Magnitude Scale
m apparent magnitude M absolute magnitude
apparent brightness of Star 1
apparent brightness of Star 2(1001/5)m1 m2
luminosity of Star 1
luminosity of Star 2(1001/5)M1 M2
related to apparent brightness related to luminosity
5 magnitudes difference = a factor of 100 in brightnessNote that a lower number means a brighter star
Ch. 11 Summary of Mathematics III
The Magnitude Scale
Note that a lower number means a brighter star
How much brighter is a 3rd magnitude star than an 8th magnitude star?
m1=8, m2=321
5
1
2
1 100
mm
b
b